Solve (x ^ 2 - 10)/(x ^ 2 - 4) + (3x)/(x ^ 2 - 4) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{x^{2}-10}{x^{2}-4}+\frac{3x}{x^{2}-4}$$

Evaluate

$\frac{x+5}{x+2}$

Short Solution Steps

Since $\frac{x^{2}-10}{x^{2}-4}$ and $\frac{3x}{x^{2}-4}$ have the same denominator, add them by adding their numerators.

$$\frac{x^{2}-10+3x}{x^{2}-4}$$

Factor the expressions that are not already factored in $\frac{x^{2}-10+3x}{x^{2}-4}$.

$$\frac{\left(x-2\right)\left(x+5\right)}{\left(x-2\right)\left(x+2\right)}$$

Cancel out $x-2$ in both numerator and denominator.

$$\frac{x+5}{x+2}$$

Expand

$\frac{x+5}{x+2}$

Short Solution Steps

Since $\frac{x^{2}-10}{x^{2}-4}$ and $\frac{3x}{x^{2}-4}$ have the same denominator, add them by adding their numerators.

$$\frac{x^{2}-10+3x}{x^{2}-4}$$

Factor the expressions that are not already factored in $\frac{x^{2}-10+3x}{x^{2}-4}$.

$$\frac{\left(x-2\right)\left(x+5\right)}{\left(x-2\right)\left(x+2\right)}$$

Cancel out $x-2$ in both numerator and denominator.

$$\frac{x+5}{x+2}$$